大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Monetary Utility Functions with Convex Level Sets.

Freddy Delbaen (ETH Zurich and University of Zurich)

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大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第62回

Monetary Utility Functions with Convex Level Sets.

Freddy Delbaen (ETH Zurich and University of Zurich)

Monetary utility functions are -- except for the expected value -- not of von Neumann-Morgenstern type. In case the utility function has convex level sets in the set of probability measures on the real line, we can give some characterisation that comes close to the vN-M form. For coherent utility functions this was solved by Ziegel. The concave case under the extra assumptions of weak compactness, was solved by Stephan Weber. Using the fact that law determined utility functions are monotone with respect to convex ordering, we could give a complete characterisation. The characterisation is similar to Weber's theorem except that we need concave functions that take the value $-\infty$. Having convex level sets can be seen as a weakened form of the independence axiom in the vN-M theory. It is a property that is related to elicitability as used in statistics.
(Joint work with Bellini, Bignozzi and Ziegel, paper accepted in Finance and Stochastics)